Theorems · Theorem · field theory

Algebra.IsAlgebraic.of_injective

∀ {R : Type u} {A : Type v} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A] {B : Type u_2}
  [inst_3 : Ring B] [inst_4 : Algebra R B] (f : A →ₐ[R] B),
  Function.Injective ⇑f → ∀ [Algebra.IsAlgebraic R B], Algebra.IsAlgebraic R A

Defined in

Mathlib.RingTheory.Algebraic.Basic

Cited by

2 results in Mathlib

Foundations

Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingRingAlgebraRingAlgebraAlgebra.IsAlgebraic